Question: Which of the following numbers is a multiple of 12? ${51,70,75,84,109}$
Answer: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $51 \div 12 = 4\text{ R }3$ $70 \div 12 = 5\text{ R }10$ $75 \div 12 = 6\text{ R }3$ $84 \div 12 = 7$ $109 \div 12 = 9\text{ R }1$ The only answer choice that leaves no remainder after the division is $84$ $ 7$ $12$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $84$. We can say that $84$ is divisible by $12$.